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SU‐E‐QI‐08: Fourier Properties of Cone Beam CT Projection
Author(s) -
Bai T,
Yan H,
Jia X,
Jiang Steve B.,
Mou X
Publication year - 2014
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.4888988
Subject(s) - fourier transform , mathematics , projection (relational algebra) , imaging phantom , fourier analysis , wedge (geometry) , cone beam computed tomography , noise (video) , mathematical analysis , physics , geometry , algorithm , computer science , optics , computer vision , image (mathematics) , computed tomography , medicine , radiology
Purpose: To explore the Fourier properties of cone beam CT (CBCT) projections and apply the property to directly estimate noise level of CBCT projections without any prior information. Methods: By utilizing the property of Bessel function, we derivate the Fourier properties of the CBCT projections for an arbitrary point object. It is found that there exists a double‐wedge shaped region in the Fourier space where the intensity is approximately zero. We further derivate the Fourier properties of independent noise added to CBCT projections. The expectation of the square of the module in any point of the Fourier space is constant and the value approximately equals to noise energy. We further validate the theory in numerical simulations for both a delta function object and a NCAT phantom with different levels of noise added. Results: Our simulation confirmed the existence of the double‐wedge shaped region in Fourier domain for the x‐ray projection image. The boundary locations of this region agree well with theoretical predictions. In the experiments of estimating noise level, the mean relative error between the theory estimation and the ground truth values is 2.697%. Conclusion: A novel theory on the Fourier properties of CBCT projections has been discovered. Accurate noise level estimation can be achieved by applying this theory directly to the measured CBCT projections. This work was supported in part by NIH(1R01CA154747‐01), NSFC((No. 61172163), Research Fund for the Doctoral Program of Higher Education of China (No. 20110201110011) and China Scholarship Council.